D.C. Del. Walter E. Fauntroy, trying to help an old political ally, took the stand in the Abscam trial yesterday and testified that Rep. John Jenrette was a man of doubtless integrity, but also a congressman with a known drinking problem.

"It was perfectly clear to me and many of my colleagues on the Hill that John was having a very serious problem with drinking," Fauntroy told the jury that is considering charges that Jenrette (D-S.C.) and a codefendant conspired to accept payoffs from representatives of phony Arab sheik in return for Jenrette's promise to introduce private immigration legislation.

"I could see it in John's cheeks and in his eyes and what I smelled on his breath that he had a problem," Fauntroy said.

The court appearance by Fauntroy, a Baptist minister and the District's lone delegate in Congress, as a character witness for Jenrette brought a unique local twist to the three-week-old trial.

Eight years ago, Fauntroy traveled to a poor, tobacco district in rural South Carolina to help a young congressional candidate garner enough black votes to defeat Rep. John L. McMillan, breaking McMillan's iron grip on the House District Committee and clearing the way for home rule in Washington.

"The theory was, we had to support a young white man for the seat," Fauntroy said, adding that Jenrette, then 36 years old, had solid roots in that South Carolina community and had "integrity that could not be attacked."

Jenrette won that primary, but was defeated in the general election. Two years later he was elected to Congress and was reelected for two more terms, each time with Fauntroy campaigning on his behalf. In return, Fauntroy testified yesterday, Jenrette "has been faithful" to his promises to support legislation and programs that affect blacks and poor people.

"The reason I've supported John Jenrette is that he has kept his word to the people who worked to get him elected," Fauntroy told the jury.

"The record speaks for itself," Fauntroy told Jenrette's attorney, Kenneth Michael Robinson. "You can test that on a vote, which I don't have but he has," Fauntroy said in an obvious reference to his own nonvoting status as the District delegate.

During the presentation of its case against Jenrette and his codefendant, John Stowe, the government has shown the jury videotapes made in late 1979 and early this year, in which Jenrette and Stowe met with an FBI undercover agent and his informant to discuss the exchange of money for Jenrette's sponsorship of the immigration bill.

One tape showed Stowe accepting $50,000 in cash from the undercover agent which he said he was taking to Jenrette's office.

Jenrette's defense contends that the congressman was suffering from the effects of alcoholism at the time of the incidents, a contention which Fauntroy's testimony about Capitol Hill knowledge of Jenrette's drinking problems was designed to buttress.

After he left the courtroom, Fauntroy said that he felt that Jenrette had been "taken advantage of," in connection with the Abscam case. He was just shot . . . he was an alcoholic," Fauntroy said.

Another member of Congress, Rep. Richard Nolan (D-Minn.), who joined Jenrette in the House for his first term in 1974, said he too recognized Jenrette's drinking problem and finally persuaded him to check into an alcohol treatment center at the Naval Medical Center in Bethesda last March. "John knew he had a drinking problem," Noland told the jury, "[but] he wouldn't admit he was an alcoholic."

In another development yesterday, Jenrette's wife, Rita, also took the witness stand and during her testimony the defense introduced a tape recording that she secretly had made last Feb. 2, the day that two FBI agents arrived at Jenrette's Capitol Hill home to inform the congressman of the Abscam sting.

According to the tape, when one of the FBI men told Jenrette that the man he thought was an agent for the sheik was actually working undercover for the FBI, Jenrette responded, "I'm glad." The defense has contended that Jenrette believed that he had become involved with organized crime forces fronting for the Arab sheiks.